British Prime Minister Theresa May cast doubt on Sunday on the effectiveness of 'points-based' immigration systems that screen applicants on the basis of factors like education and skills, setting up a potential conflict with some of her own ministers.

Foreign minister Boris Johnson and trade minister Liam Fox were part of the 'Brexit' camp that argued that voting to leave the European Union would free Britain from the duty to admit all EU nationals who want to live and work here, enabling it to cut immigration by introducing an Australian-style points system.

May, who favored staying in the EU but has promised to deliver on the June 23 referendum vote by steering Britain out of the bloc and tightening border controls, said such systems were difficult to manage.

"One of the issues is whether or not points-based systems do work," she told reporters on her way to a G20 summit in China, citing her experience as Britain's longest-serving interior minister in over 50 years.

"There is no single silver bullet that is the answer in terms of dealing with immigration."

The comments offer the first glimpse into May's stance on the hardest conundrum thrown up by the referendum: how to tighten border controls with the EU without losing access to its single market.

Its 27 partners are so far adamant that it cannot enjoy full trade benefits unless it continues to let in EU nationals as before.

Watered-down Brexit

The prime minister risks upsetting key members of the team she assembled in July to deliver an EU exit that protects Britain's global standing and carves out a new role for the country at the vanguard of global free trade.

Speaking in June before he was appointed as foreign minister, Johnson - figurehead of the Leave campaign and May's one-time rival for the prime minister's job - said a points-based system could bring back democratic control and better meet businesses' needs.

May's words will fuel fears among voters and Eurosceptic lawmakers that having a pro-Remain prime minister in charge will result in a watered-down version of Brexit that does not represent what people voted for.

May also declined to commit, when asked, to Leave campaign promises to increase healthcare spending and reduce energy taxes.

Asked whether immigration controls precluded access to the single market, May said she was optimistic about what sort of deal Britain could negotiate.

"I want to be ambitious with what we can achieve, I don't take anything for granted, I'm going out there to get the best possible deal."